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Corrections to Sextant   Time   Finding GHA and Declination   Assumed Position and Local Hour Angle   Computed Altitude and Azimuth    Interpolation    Altitude Intercept    Using Position Plotting Sheets    Plotting Lines of Position

ABOUT THIS COURSE AND HOW TO USE IT.  

THIS COURSE IS DESIGNED TO HELP YOU PREPARE YOURSELF TO PASS THE U. S. COAST GUARD  EXAMINATION ON CELESTIAL NAVIGATION FOR THE UPON OCEANS ENDORSEMENT.

FORMAL TEXTBOOKS INTENDED FOR USE IN COLLEGE CLASSROOMS DEVOTE MORE SPACE THAN NECESSARY TO ASTRONOMY AND HISTORY AND ARE OFTEN WRITTEN ON THE ASSUMPTION THAT THE STUDENT HAS A COMMAND OF SPHERICAL TRIGONOMETRY. FURTHERMORE, THEY SOMETIMES OMIT CERTAIN TECHNIQUES REQUIRED FOR THE COAST GUARD TEST. SEVERAL EXCELLENT BOOKS WRITTEN FOR YACHTSMEN LEAVE OUT EVEN MORE THINGS YOU MUST KNOW FOR THE TEST AND ENCOURAGE THE STUDENT TO BE SATISFIED WITH APPROXIMATE ANSWERS. IT IS TRUE THAT A CASUAL APPROACH TO THE COMPUTATIONS IS ACCEPTABLE WHEN THE BASIC MEASUREMENT, THE SEXTANT OBSERVATION, ISN'T ALL THAT ACCURATE WHEN TAKEN FROM A SMALL BOAT BY A WET NAVIGATOR BUT THE PERSON WHO WRITES THE TEST QUESTIONS DOESN'T SUFFER FROM INACCURACY. HE STARTS WITH A PRECISE NUMBER OR POINT ON A CHART AND BUILDS A PROBLEM WORKING TO A PRECISION OF ONE TENTH OF A MINUTE OF LATITUDE AND LONGITUDE. IF YOU WORK THE PROBLEM CORRECTLY TO THE SAME DEGREE OF PRECISION YOU SHOULD ARRIVE AT THE ANSWER HE STARTED WITH (PLUS OR MINUS ONE TENTH OF A MINUTE. ALL THE EXAMINER CAN DO IS COMPARE YOUR ANSWER WITH THE WRITER’S.

THIS COURSE WAS WRITTEN WITH THESE GOALS IN MIND. 

   WHEN YOU ARE READY FOR THE TEST, YOU'LL ALSO BE READY TO DO CELESTIAL NAVIGATION ANYWHERE IN THE WORLD AFTER YOU'VE HAD SOME PRACTICE WITH A SEXTANT. FOR PRACTICAL NAVIGATION YOU COULD GET BY WITH LESS KNOWLEDGE THEN YOU'LL NEED FOR THE TEST.  

   YOU WON'T NEED A SEXTANT FOR THIS COURSE OR FOR THE TEST. NOBODY CAN TEACH YOU HOW TO USE ONE ANYWAY. SKILL WITH A SEXTANT IS A PERSONAL MECHANICAL SKILL THAT CAN ONLY BE ACQUIRED BY PRACTICE. IT ISN'T HARD. WHEN YOU'RE READY, GET SOMEONE TO SHOW YOU HOW TO HOLD ONE, THEN START MAKING OBSERVATIONS FROM A KNOWN POSITION. AN EXCELLENT WAY TO DO IT IS TO MAKE YOUR OBSERVATION THEN GET LORAN OR GPS FIXES IMMEDIATELY AFTERWARD. WORK OUT AND PLOT BOTH FIXES. WHEN YOUR CELESTIAL FIXES AND GPS FIXES COME OUT RELATIVELY CLOSE TOGETHER THEN YOU CAN LOOK ANYONE IN THE EYE AND TELL THEM YOU’RE A NAVIGATOR.  

   THE COAST GUARD TEST CONSISTS OF TEN MULTIPLE CHOICE QUESTIONS. THAT ISN'T AS SHORT AS IT SOUNDS. YOU MAY HAVE TO WORK FIVE OR SIX PROBLEMS TO GET THE ANSWER TO A SINGLE QUESTION. THE PASSING SCORE IS 90%. EACH QUESTION IS INDEPENDENT. IF YOU GET ONE WRONG, IT WILL NOT AFFECT ANOTHER QUESTION. SOME OF THE WRONG CHOICES ARE ARRIVED AT BY WORKING THE PROBLEM AND DELIBERATELY MAKING A COMMON MISTAKE,  SUCH AS TAKING DATA FROM THE WRONG PAGE IN THE ALMANAC. THE FACT THAT ANSWER MATCHES ONE OF THE CHOICES DOES NOT PROVE THAT YOU'RE RIGHT. 

   ANSWERS MUST FALL WITHIN THE FOLLOWING TOLERANCES:

WHEN THE PROBLEM INVOLVES ONLY CALCULATIONS (NO PLOTTING) GHA, LHA, DECLINATION, HO, HC, ETC.: DATA EXPRESSED TO ONE TENTH OF A MINUTE OF ARC IN THE TABLES. ALSO, ANSWERS REACHED BY USING THIS DATA.   

ZN, A, ETC.: DATA EXPRESSED TO ONE TENTH OF A DEGREE THE TABLES.   (PLUS OR MINUS 0.1° ) 

WHEN THE SOLUTION OF A PROBLEM REQUIRES PLOTTING ON A CHART:

   SOME OF THE TERMS USED ABOVE MAY NOT MEAN ANYTHING TO YOU YET. THEY WILL. WHEN YOUR ANSWERS ARE THAT CLOSE TO THE GIVEN ANSWERS TO THE PRACTICE PROBLEMS IN THIS COURSE, YOUR WORK WILL BE  SATISFACTORY. AT LEAST SOME OF THE TEST QUESTIONS ALLOW A BIT MORE SLACK, BUT IF YOU WORK WITHIN THESE TOLERANCES, YOU CAN BE SURE THAT YOUR ERRORS ARE SMALL ENOUGH. THERE IS NO "OFFICIAL" TIME LIMIT FOR THE TEST, BUT IT COMES IN ONE PIECE SO IT'S NECESSARY TO COMPLETE IT DURING THE EXAMINERS' WORKING HOURS IN ONE DAY. THAT IS MORE THAN ENOUGH TIME IF YOU'RE PREPARED, BUT DON'T WALK INTO THE COAST GUARD OFFICE AT 1400 AND EXPECT TO FINISH THAT DAY. WHEN YOU TEST, PLAN ON BEING THERE WHEN THEY OPEN AND BE READY FOR A GOOD DAY'S WORK. WE RECOMMEND THAT YOU WORK EACH PROBLEM TWICE AS A DOUBLE CHECK, DOING IT THE SECOND TIME ON FRESH PAPER WITHOUT LOOKING AT THE FIRST ONE. IT MIGHT TAKE AN EXPERIENCED NAVIGATOR THREE OR FOUR HOURS TO COMPLETE TEN PROBLEMS THAT WAY.  

THE COAST GUARD HAS SEVERAL VERSIONS OF THE TEST. EACH ONE HAS TEN QUESTIONS SELECTED FROM THE FOLLOWING TYPES OF QUESTIONS. YOU WON'T GET ALL TYPES OF QUESTIONS ON ANY COPY OF THE TEST, BUT YOU ARE RESPONSIBLE FOR ANY OF THEM.

  1. SIGHT REDUCTION—SUN

  2. SIGHT REDUCTION---STAR

  3. STAR FIXES

  4. RUNNING FIXES

  5. LATITUDE BY MERIDIAN ALTITUDE---UPPER MERIDIAN

  6. LATITUDE BY POLARIS

  7. TIME OF LOCAL APPARENT NOON

  8. TIME OF SUNRISE

  9. TIME OF SUNSET

  10. DEVIATION OR GYRO ERROR BY AZIMUTH

  11. DEVIATION OR GYRO ERROR BY AMPLITUDE

  12. IDENTIFICATION OF UNKNOWN STARS

  13. SELECTION OF STARS FOR BEST FIX

  14. CORRECTION OF SEXTANT ALTITUDE

  15. ETA PROBLEMS

  16. TIME TICK PROBLEMS

  17. R.D.F. PROBLEMS

  18. OMEGA PROBLEMS

  19. LORAN FIX USING LORAN CHARTLET.  

   THIS COURSE CONTAINS THE INSTRUCTIONS FOR DOING ALL THOSE PROBLEMS.  YOU SHOULD HAVE A COMPLETE COPY OF H.0.229 15° THRU 30° INCLUSIVE AND A REPRINT OF THE 1981 NAUTICAL ALMANAC TO WORK ALL THE PROBLEMS IN THIS WEB AS WELL AS ALL THE CELESTIAL PROBLEMS IN THE ONLINE STUDY ROOM. A SUPPLY OF POSITION PLOTTING SHEETS, AND A STAR FINDER. ALL YOU WILL NEED TO COMPLETE YOUR KIT IS YOUR FAVORITE PLOTTING TOOLS (DIVIDERS AND PARALLEL RULES OR EQUIVALENT). AN INEXPENSIVE CALCULATOR ISN'T ABSOLUTELY NECESSARY, BUT YOU WILL FIND ONE VERY USEFUL. A SET OF TRIANGLES FOR DRAWING LINES OF POSITION. ANY DRAWING TOOL YOU CAN USE TO DRAW A LINE AT RIGHT ANGLES TO ANOTHER LINE WILL DO. ONE MORE THING--GET A GOOD SUPPLY OF SCRATCH PAPER. BUY THE CHEAP STUFF AND PLENTY OF IT. IT'S BETTER TO USE LOOSE SHEETS OR THE KIND OF TABLET THAT MAKES IT EASY TO TEAR OFF A SCRATCH SHEET AND THROW IT AWAY. YOU ARE BOUND TO MAKE MISTAKES IN YOUR PRACTICE WORK AT FIRST. IF YOU MAKE THEM IN A BOUND WORKBOOK OR SPIRAL NOTEBOOK, YOU TEND TO KEEP THEM AND REVIEW THEM LIKE NOTES. YOU DON'T WANT TO REVIEW MISTAKES. ALL OF THE ABOVE MENTIONED  BOOKS AND TOOLS CAN BE FOUND AT MARINE EDUCATION TEXTBOOKS CATALOG , OF WHICH I HAVE ABSOLUTELY NO AFFILIATION, OR ORDERED FROM MOST NAUTICAL SUPPLY HOUSES

   WHAT SKILLS DO YOU NEED TO GET STARTED WITH THE COURSE? IF YOU CAN DO THE SAME KIND OF DR PLOTTING YOU DID FOR YOUR LICENSE, CAN DO ORDINARY ARITHMETIC, AND HAVE ENOUGH MECHANICAL ABILITY TO, OPERATE A PENCIL SHARPENER AND CARE ENOUGH TO OPERATE IT OFTEN YOU CAN HANDLE THIS COURSE.  IF YOU HAVE ALWAYS USED A NAUTICAL SLIDE RULE TO WORK THE TIME   SPEED AND DISTANCE CALCULATION OF DR PLOTTING, IT WILL PAY TO YOU TO LEARN TO DO THEM WITH A CALCULATOR INSTEAD.  

   WHAT IS THE BEST WAY TO WORK THROUGH THIS COURSE? HERE ARE SOME RECOMMENDATIONS.

  1. DO THE LESSONS IN THE ORDER THEY COME IN THE BOOK. WITH VERY FEW EXCEPTIONS, UNDERSTANDING OF A GIVEN LESSON DEPENDS ON KNOWING THE MATERIAL COVERED IN EARLIER LESSONS. IF YOU SKIP AROUND, YOU WILL GET LOST.                         

  1. IF YOU HAVE STUDIED CELESTIAL NAVIGATION BEFORE IT MAY BE THAT YOU CAN AFFORD TO SKIP SOME OF THE EXPLANATIONS. YOU CAN FIND OUT BY GOING DIRECTLY TO THE PRACTICE PROBLEMS AT THE END OF THE LESSON. IF YOU GET ALL OF THEM RIGHT, FINE. CARRY ON. IF YOU DON’T THEN GO BACK AND START THE LESSON FROM SCRATCH. IT COULD BE THAT YOU ARE JUST RUSTY OR IT COULD BE THAT THE METHODS YOU ALREADY KNOW ARE GOOD ENOUGH FOR PRACTICAL NAVIGATION BUT NOT GOOD ENOUGH FOR THE PRECISION REQUIRED TO PASS THE COAST GUARD EXAM.

  1. WHEN YOU WORK PRACTICE PROBLEMS, CHECK THE ANSWER TO EACH ONE AS YOU FINISH IT. IF YOU ARE CORRECT, PROCEED. IF YOU AREN'T: READ THE EXPLANATION AGAIN AND THEN REWORK THE SAME PROBLEM FROM SCRATCH. DO NOT WORK A WHOLE SERIES OF PROBLEMS AND THEN CHECK THE ANSWERS. YOU COULD BE MAKING THE SAME MISTAKE OVER AND OVER, THEREBY FORMING A BAD HABIT.  

  1. WORK IN QUIET PLACES WITH GOOD LIGHT. AN HOUR OF STUDY IN FAVORABLE CONDITIONS IS WORTH THREE OR FOUR HOURS TRYING TO WORK WITH DISTRACTIONS. 

  1. TAKE IT IN SMALL DOSES. IF YOU TRY TO STUDY MORE THAN TWO OR THREE HOURS AT A TIME, THE LAST HOUR DOESN'T DO YOU HALF AS MUCH GOOD AS THE FIRST ONE.  

  1. WHEN YOU GET CONFUSED STOP AND TAKE A BREAK! 

  1. WHEN YOU MAKE A MISTAKE DON’T WAIST TIME LOOKING FOR IT. THROW AWAY. TAKE A LITTLE BREAK IF EVEN ONLY FOR A MINUTE. THEN TAKE A FRESH SHEET OF PAPER AND START OVER. IT’S HARD TO CONVINCE PEOPLE TO DO THIS. SCRATCH PADS ARE JUST ABOUT THE CHEAPEST AND MOST USEFUL THINGS YOU CAN BUY. GET STACKS OF THEM AND USE THEM LAVISHLY.  

  1. REVIEW FROM TIME TO TIME. THE BEST WAY TO REVIEW IS TO GO BACK AND WORK SOME OF THE PRACTICE PROBLEMS IN THE EARLIER LESSONS YOU'VE ALREADY FINISHED. IF YOU CAN STILL DO THEM, THERE IS NO NEED TO READ THE EXPLANATIONS AGAIN. IF YOU HAVE FORGOTTEN SOMETHING, IT'S BETTER TO FIND OUT RIGHT THEN AND RELEARN IT THAN TO PRESS ON AND JUST GET MORE CONFUSED. THE REVIEW GETS EASIER AND MORE PRODUCTIVE EACH TIME YOU REPEAT IT.  

  2.  NEATNESS COUNTS!!! TAKING THE TIME TO WRITE OR PRINT YOUR BEST AND KEEPING COLUMNS OF NUMBERS AND THERE DECIMAL POINTS NEATLY ALIGNED AND BEING PARTICULAR ABOUT LABELS AND SYMBOLS HELPS TO KEEP YOUR THINKING MORE ORDERLY AND PREVENTS A LOT OF MISTAKES.  

  3. THE LAST RECOMMENDATION IS: THAT WHEN YOU REVIEW, REVIEW THIS ALSO.  

   WHAT CAN YOU DO IF YOU GET BOGGED DOWN AND WANT SOME HELP? ONE THING YOU CAN DO IS TO CONSULT A DIFFERENT EXPERT. IT MAY HELP TO REVIEW ANOTHER AUTHOR’S EXPLANATION OF THE SAME FACTS. OF ALL TEXTS AND SELF STUDY COURSES, ONE STANDS ABOVE ALL THE REST: 

PRIMER OF NAVIGATION, 

GEORGE W. MIXTER, AUTHOR. 

VAN NOSTRAND, PUBLISHER.  

   AMONG  NAVIGATORS, IT’S REFERRED TO AS –“THE MIXTER”, MUCH AS WE SAY “THE BOWDITCH” OR “THE BIBLE.” BE SURE YOU GET A SIXTH OR LATER EDITION. THE EARLIER EDITIONS DON’T EXPLAIN PUBLICATION NO. 229, WHICH YOU WILL HAVE TO USE IN THIS COURSE AND FOR THE TEST. I DON’T RECOMMEND BOWDITCH ON NAVIGATION FOR BEGINNERS. IT WAS NEVER INTENDED TO BE A TEXTBOOK, ALTHOUGH IT’S VERY USEFUL AS A REFERENCE ONCE YOU UNDERSTAND THE SUBJECT.

WORK FORMS, TERMS, AND ABBREVIATIONS

   “THE FORM WORKS THE PROBLEM”   THAT QUOTE HAS BEEN USED BY NAVIGATION INSTRUCTORS SINCE BEFORE THE SEXTANT WAS INVENTED. MANY HAVE BECOME SUCCESSFUL CELESTIAL NAVIGATORS WITH ONLY A COUPLE OF DAYS OF INSTRUCTION. THEY WERE SENT TO SEA WITH A SUPPLY OF PREPARED FORMS WITH THE DIRECTIONS PRINTED ON THEM. YOU COULD DO THAT, TOO, BUT YOU CAN'T HAVE PREPARED FORMS IN THE EXAMINATION ROOM YOU'LL HAVE JUST THE BOOKS AND BLANK PAPER SHOULD YOU MAKE A PROJECT OF MEMORIZING A SET OF FORMS FIRST? DEFINITELY NOT. IT CAN PROBABLY BE DONE, BUT IT WOULD BE A WASTE OF TIME. YOU NEED TO WORK PRACTICE PROBLEMS ANYWAY. AS YOU WORK THEM, PUT THEM DOWN IN THE RECOMMENDED FORM EACH TIME. YOU'LL FIND AFTER A WHILE THAT YOU'VE LEARNED THE FORMS WITHOUT ANY EXTRA TIME AND EFFORT. THIS IS IMPORTANT ENOUGH TO SAY AGAIN: “THE FORM WORKS THE PROBLEM” THE FEW EXTRA SECONDS YOU SPEND SETTING DOWN THE FORM EVERY TIME YOU WORK A PROBLEM WILL SAVE YOU MANY HOURS AND MUCH CONFUSION IN THE LONG RUN. 

    AS YOU GAIN EXPERIENCE YOU MAY MODIFY SOME OF THE FORMS TO SUIT YOURSELF.  MOST NAVIGATORS DO THAT EVENTUALLY. THERE IS NOTHING MAGIC ABOUT THE PARTICULAR FORMS USED IN THIS COURSE. WHAT IS IMPORTANT IS THAT YOU USE SOME KIND OF FORM TO KEEP YOUR WORK ORDERLY AND AVOID CONFUSION. START WITH THE FORMS USED IN THIS WEB. SHORTCUTS ARE NOT FOR BEGINNERS. MUCH THE SAME CAN BE SAID FOR STICKING WITH STANDARD TERMS, ABBREVIATIONS, LABELS AND SYMBOLS. THEY HELP TO KEEP YOU STRAIGHT. YOU MUST KNOW THEM TO BE ABLE TO READ THE TEST PROBLEMS. IF YOU DON'T KNOW THE MEANING OF “Hc”, “Ho’, “Zn”, "a", ETC., YOU WON'T STAND A CHANCE. AUTHORS OF “HOW TO” BOOKS ON NAVIGATION WRITTEN FOR AMATEURS SOMETIMES INVENT THEIR OWN TERMS. FOR EXAMPLE THE TERM “GEOGRAPHICAL POSITION” (G.P.) IS USED IN U.S. GOVERNMENT PUBLICATIONS. IT MEANS THE POINT WHERE A LINE DRAWN FROM A CELESTIAL BODY TO THE EARTH'S CENTER PASSES THROUGH THE EARTH'S SURFACE.  THE TEST WILL PUT THE QUESTIONS IN THE “OFFICIAL” WORDS USED IN GOVERNMENT PUBLICATIONS. FOR THAT REASON, THIS COURSE USES  THE "OFFICIAL" TERMS AND THE STANDARD SYMBOLS AND ABBREVIATIONS.  WILL YOU HAVE TO MEMORIZE ALL THE TERMS AND ABBREVIATIONS?  CERTAINLY, BUT DON'T MAKE A PROJECT OF MEMORIZING A LIST. AS NEW TERMS ARE INTRODUCED I WILL LINK THEM TO A GLOSSARY WHERE YOU CAN REFRESH YOUR MEMORY.

   IN ADDITION TO PAYING ATTENTION TO THE TERMS AND DEFINITIONS, IT IS ESSENTIAL TO PUT “NAMES” ON THE NUMBERS. "DEVIATION 14" MEANS NOTHING. "DEVIATION 14 W" MEANS SOMETHING EXACT, THE NAME, "W" (WEST), MAKES ALL THE DIFFERENCE. IN NAVIGATION PROBLEMS, THE NAME OF A VALUE (N OR S, E OR W) VERY OFTEN TELLS YOU WHETHER TO ADD OR SUBTRACT THE NUMBER.  WRITE THE NAME DOWN EVERY TIME.

WHAT ACTUALLY HAPPENS AT SEA

   FORTY OR FIFTY YEARS AGO, MOST SHIPS OUT OF SIGHT OF LAND HAD NO WAY TO FIND THEIR POSITION EXCEPT BY DEAD RECKONING AND CELESTIAL NAVIGATION. IT STILL HAPPENS. YOUR LORAN, GPS, SATELLITE NAVIGATOR, RADAR, OR GENERATOR CAN GO DOWN. DEAD RECKONING IS FINE FOR A DAY OR TWO, BUT THE LONGER YOU GO WITHOUT A FIX THE MORE DOUBTFUL YOUR DR BECOMES. AFTER A SPELL OF HEAVY WEATHER, IT'S PROBABLY NO BETTER THAN A FANCY GUESS. THAT'S WHY THE COAST GUARD REQUIRES YOU TO KNOW CELESTIAL NAVIGATION TO OPERATE MORE THAN 200 MILES OFFSHORE. WITH A SEXTANT, A GOOD TIMEPIECE, A COUPLE OF BOOKS AND A "PENCIL, YOU CAN GET YOUR POSITION ACCURATELY ENOUGH. THIS GEAR EVEN WORKS WITHOUT ELECTRICITY. IT WILL EVEN WORK IN A LIFEBOAT. THE PURPOSE OF THE BOOK IS TO HELP YOU LEARN. IT'S EASIER TO LEARN IF YOU BELIEVE THE INFORMATION IS USEFUL. YOU CAN DO MORE WITH IT THAN JUST GET YOUR LICENSE ENDORSED. IT'S IMPORTANT TO THE SAFE AND EFFICIENT OPERATION OF YOUR VESSEL. IT'S IMPORTANT TO YOUR CAREER. AND IT'S NOT THAT TOUGH. LET'S TAKE A QUICK LOOK AT WHAT CAN BE PERFORMED WITH A KNOWLEDGE OF CELESTIAL NAVIGATION.  

   A LITTLE BEFORE SUNRISE, WHEN THE NAVIGATOR CAN SEE THE STARS AND THE HORIZON AT THE SAME TIME, HE MEASURES THE VERTICAL ANGLES BETWEEN  TWO OR MORE STARS AND THE HORIZON WITH HIS SEXTANT. BE NOTES THE EXACT TIME HE MEASURES EACH ANGLE. THIS ONLY TAKES A FEW MINUTES. IT HAS TO BE DONE PRETTY QUICKLY. AFTER THE SUN IS UP YOU CAN'T SEE THE STARS.

   NOW HE CAN GO TO WORK IN THE AIR CONDITIONED COMFORT OF THE WHEELHOUSE. HE PLOTS A DR FOR THE TIME HE SHOT THE STARS. THEN HE CONVERTS THE TIME OF EACH SHOT TO THE DATE AND TIME IN THE ZONE OF GREENWICH, ENGLAND. THESE TIMES ARE USED TO LOOK UP THE EXACT LOCATION OF THE STARS IN THE NAUTICAL ALMANAC. HE ALSO MAKES SOME CORRECTIONS TO THE SEXTANT READINGS FROM THE ALMANAC, AND PUTS IT AWAY. THE INFORMATION FROM THE ALMANAC IS USED TO LOOK UP SOME NUMBERS IN ANOTHER BOOK, THE "SIGHT REDUCTION TABLES." THESE TELL HIM EXACTLY WHAT DIRECTION FROM HIM AND HOW HIGH IN THE SKY THE STARS WOULD HAVE BEEN IF HE HAD BEEN EXACTLY WHERE HE THOUGHT HE WAS. HE COMPARES THESE ANSWERS TO HIS CORRECTED SEXTANT READINGS AND PLOTS THE RESULTS ON THE CHART FOR A FIX. THAT PART MIGHT TAKE AN HOUR IF THE NAVIGATOR IS RUSTY. NO FANCY MATH IS NEEDED--JUST PLAIN ARITHMETIC. ABOUT MID-MORNING HE'LL SHOOT THE SUN IF IT'S OUT. HE CAN WORK THE ARITHMETIC RIGHT THEN OR SAVE IT FOR LATER. NOW HE CAN FIGURE THE TIME OF "LOCAL APPARENT NOON," WHEN THE BOAT AND THE SUN WILL MEET AT THE SAME LONGITUDE.  IT WILL BE VERY HANDY TO SHOOT THE SUN AGAIN AT THAT TIME. IT PROVIDES A QUICK, EASY SOLUTION FOR LATITUDE, AND THE LATITUDE WILL BE ACCURATE EVEN IF HIS TIMEPIECE IS OFF. WITH THE MORNING AND NOON SUN SIGHTS, HE CAN GET A HANDY AND ACCURATE RUNNING FIX SOME TIME DURING THE DAY HE SHOULD TAKE AN ACCURATE COMPASS BEARING OF THE SUN AND NOTE THE EXACT TIME. HE CAN USE HIS BOOKS TO FIGURE WHAT ITS TRUE BEARING WAS AT THAT INSTANT AND COMPARE THAT WITH THE COMPASS BEARING TO DETERMINE DEVIATION OR GYRO ERROR. HE HAS TWO WAYS TO DO THIS. ONE METHOD CAN BE USED ANY TIME AND USES THE SAME BOOKS, BUT REQUIRES AN EXTRA INSTRUMENT, AN AZIMUTH CIRCLE. THE OTHER CAN ONLY BE DONE AT SUNRISE OR SUNSET AND TAKES A THIRD BOOK, BUT  REQUIRES NO SPECIAL INSTRUMENT HE MIGHT SHOOT THE SUN IN MID-AFTERNOON JUST IN CASE IT GETS CLOUDY AFTER SUNSET SO HE CAN'T SEE THE EVENING STARS. HE CAN ALWAYS PREDICT THE TIME OF SUNRISE OR SUNSET SO HE DOESN'T HAVE TO STAY UP WAITING FOR THEM; JUST TELL THE WATCH WHEN TO WAKE HIM AND HOW HE WANTS HIS COFFEE.  IF POLARIS (THE NORTH STAR) CAN BE SEEN AT STAR TIME, HE CAN TAKE ADVANTAGE OF AN EASY SOLUTION FOR LATITUDE AND A TRUE BEARING FOR A COMPASS CHECK.  TO USE STARS, HE HAS TO KNOW THEIR NAMES, BUT HE DOESN'T HAVE TO BE AN ASTRONOMER TO REMEMBER THEM. THE ALMANAC AND A SIMPLE PLASTIC "STAR FINDER" MAKE SHORT WORK OF NAMING THE STARS. WHEN YOU'VE FINISHED THIS COURSE, YOU'LL KNOW HOW TO DO ALL THESE THINGS. IT WILL BE MORE THAN ENOUGH TO DO A GOOD JOB OF OFFSHORE NAVIGATION. AND IT'S JUST RIGHT FOR THE COAST GUARD TEST. )

(THE BIG PICTURE)

   YOU CAN PERFORM THE SAME “MAGIC” AS THE NAVIGATOR ABOVE WITHOUT UNDERSTANDING CELESTIAL NAVIGATION AT ALL. YOU COULD FILL IN THE BLANKS AND FOLLOW THE DIRECTIONS ON READY-MADE FORMS. A LOT OF PEOPLE DO IT THAT WAY. BUT THE COAST GUARD WON'T LET YOU HAVE THE FORMS. YOU'LL HAVE TO MEMORIZE THE PROCEDURES AND ALL THE TERMS AND THEIR ABBREVIATIONS TO MAKE SENSE OF THE TEST PROBLEMS. THAT WOULD BE AN ENORMOUS JOB IF THEY DIDN'T MEAN ANYTHING TO YOU. IT WILL BE MUCH EASIER IF YOU FIRST UNDERSTAND THE MEANING OF THINGS LIKE “GHA” AND “DEC.” IF YOU DIDN'T KNOW WHAT “LHA” STOOD FOR, AND WHY IT CAN'T BE MORE THAN 360 DEGREES, YOU COULD PLUG SOME IMPOSSIBLE NUMBERS INTO YOUR FORM AND NOT REALIZE ANYTHING WAS WRONG. THAT'S WHY YOU NEED TO UNDERSTAND “THE BIG PICTURE.”

   YOU KNOW THAT THE EARTH AND OTHER PLANETS TRAVEL IN ORBIT AROUND THE SUN AND SPIN AT THE SAME TIME. THE MOON ORBITS THE EARTH AND THE STARS ARE SCATTERED ALL OVER ZILLIONS OF MILES AWAY.  BUT FROM WHERE WE STAND, IT SURE LOOKS LIKE THOSE HEAVENLY BODIES ARE ON THE INSIDE OF A GREAT HOLLOW BALL WHICH SURROUNDS THE EARTH AND ROTATES EAST TO WEST AT ONE REVOLUTION EVERY TWENTY-FOUR HOURS. THAT IMAGINARY BALL, CALLED THE “CELESTIAL SPHERE” IS THE BASIS OF NAUTICAL ASTRONOMY. IT'S JUST A HANDY WAY TO PREDICT WHERE A BODY IS RELATIVE TO THE EARTH AT ANY TIME.  

IMAGE1 IS A CUTAWAY VIEW OF THE EARTH AND THE CELESTIAL SPHERE.

VIEW IMAGE1

   YOU CAN SEE THAT THE “EARTHLY” LINES OF LATITUDE AND LONGITUDE ARE DUPLICATED ON THE CELESTIAL SPHERE, BUT THEY ARE GIVEN DIFFERENT NAMES. POSITION A ON THE EARTH HAS THE COORDINATES OF LATITUDE 70°N, LONGITUDE 60°W.

THE LOCATION OF A STAR DIRECTLY ABOVE POSITION A WOULD BE EXPRESSED IN TERMS OF DECLINATION. (DEC.), AND GREENWICH HOUR ANGLE, (GHA). DECLINATION IS MEASURED IN THE SAME WAY AS LATITUDE NORTH OR SOUTH OF A 0° REFERENCE LINE CORRESPONDING TO THE EQUATOR.

A STAR DIRECTLY ABOVE POSITION "A" WOULD THEREFORE HAVE A DEC. OF NORTH 70°.

THE GREENWICH HOUR ANGLE IS THE CELESTIAL SPHERE'S EQUIVALENT OF LONGITUDE, BUT IT IS MEASURED ONLY WESTWARD FROM GREENWICH. GHA CAN BE AS MUCH AS 359° -59.9'. A STAR DIRECTLY ABOVE POSITION A (LONGITUDE 60° W) WOULD THEREFORE HAVE A GHA OF 60°. (NOTICE THAT IT IS NOT NECESSARY TO DESCRIBE A GHA AS EAST OR WEST, BECAUSE IT IS ALWAYS WEST OF GREENWICH.)

LET'S NOW SEE IF WE CAN USE THESE NEW TERMS OF REFERENCE TO LOCATE A STAR DIRECTLY ABOVE POSITION "B', WHICH HAS EARTHLY COORDINATES OF 60°N, 30°E. THE DECLINATION OF THE STAR IS SIMPLE. IT MATCHES THE LATITUDE EXACTLY AND WOULD BE EXPRESSED AS DEC. NORTH 60°.

   REMEMBERING THAT GHA IS MEASURED ONLY WESTWARD FROM THE PRIME MERIDIAN, CAN YOU DETERMINE THE GHA OF THE STAR? COUNTING THE DEGREES WEST FROM THE PRIME MERIDIAN, YOU WILL FIND THAT A GHA. OF 330° IS EQUIVALENT TO 30°E LONGITUDE. TO REVIEW, THE LOCATION OF A CELESTIAL BODY ON THE CELESTIAL SPHERE IS EXPRESSED IN TERMS OF DECLINATION AND GREENWICH HOUR ANGLE. DECLINATION CORRESPONDS TO LATITUDE, AND GHA IS SIMILAR TO LONGITUDE EXCEPT THAT IT IS MEASURED ONLY WESTWARD FROM GREENWICH.

  LET'S NOW CUT BOTH THE EARTH AND THE CELESTIAL SPHERE ALONG THE LINE FROM A TO B TO LEARN SOME OTHER TERMS. IN THE CUTAWAY DRAWING ON IMAGE2.

VIEW IMAGE2

   WE SEE A SHIP LOCATED AT POSITION "A" ON THE EARTH AND A STAR LOCATED AT POSITION "B" ON THE CELESTIAL SPHERE. THE POINT DIRECTLY ABOVE THE SHIP IS CALLED THE “ZENITH” THE ANGLE FROM THE ZENITH TO THE STAR IS THEREFORE CALLED THE “ZENITH DISTANCE”, WHICH IS ABBREVIATED AS “z” THE ANGLE THAT YOU OBTAIN WHEN “SHOOTING’ A STAR WITH A SEXTANT IS CALLED THE “OBSERVED ALTITUDE” WHICH IS ABBREVIATED AS “Ho” IT IS THE ANGLE UP FROM THE “CELESTIAL HORIZON” TO THE STAR. THE CELESTIAL HORIZON IS ALWAYS AT A RIGHT ANGLE (90°) FROM THE ZENITH. NOW YOU KNOW THAT “z” (ZENITH DISTANCE) IS THE ANGLE FROM THE ZENITH TO THE STAR! “Ho” (OBSERVED ALTITUDE) IS THE ANGLE FROM THE CELESTIAL HORIZON TO THE STAR. BOTH ANGLES ADDED TOGETHER EQUAL 90° DEGREES. YOU CAN THEREFORE SAY THAT “z” EQUALS 90° MINUS “Ho”. SIMILARLY, “Ho” EQUALS 90° MINUS “z”. THERE IS ANOTHER POINT ON THE DIAGRAM THAT WILL BE IMPORTANT TO YOU. THE POINT ON THE EARTH THAT IS DIRECTLY BELOW THE STAR IS CALLED THE “GEOGRAPHICAL POSITION” OF THE STAR, ABBREVIATED "G.P." THE G.P. IS WHERE THE STAR WOULD LAND IF IT FELL DIRECTLY TO THE EARTH. THE LINE FROM THE SHIP TO THE G.P. IS A GREAT CIRCLE. ONE DEGREE OF A GREAT CIRCLE ON EARTH EQUALS SIXTY NAUTICAL MILES. IF “Ho” WAS 40°, “z” WOULD BE 50°. (90° -40° = 50°) THE G.P. MUST BE 50 X 60 MILES, OR 3000 MILES FROM THE SHIP. IF YOU HAD A BIG ENOUGH CHART, YOU COULD PLOT THE G.P. AND THEN DRAW A CIRCLE AROUND IT AT A DISTANCE OF 3000 MILES. THE SHIP'S POSITION WOULD BE SOMEWHERE ON THAT CIRCLE.  

   THE CIRCLE WOULD BE A LINE OF POSITION. IT WOULD BE THE SAME THING AS TAKING A RADAR RANGE TO A LIGHTHOUSE AND DRAWING AN ARC OF THAT RADIUS FOR A LINE OF POSITION. WHEN THE SHIP AND THE G.P. ARE CLOSE ENOUGH TO LIE ON THE SAME CHART, THAT IS EXACTLY WHAT YOU DO. IT DOESN'T HAPPEN OFTEN. IT CAN HAPPEN ONLY WHEN THE BODY IS WITHIN THREE OR FOUR DEGREES OF THE ZENITH, AND IT'S VERY DIFFICULT TO GET AN ACCURATE SEXTANT READING OF SOMETHING ALMOST OVERHEAD FROM A MOVING BOAT. MOST OF THE TIME YOU GET THE SAME RESULT INDIRECTLY USING THE FOLLOWING METHOD THAT IS BASED ON THE SAME PRINCIPLE.

  THIS PICTURE SHOWS THE ANGLES WE'VE DISCUSSED “IMAGE3” (EXCEPT Ho), AS THEY WOULD APPEAR DRAWN ON A GLOBE. THE ELEVATED POLE, THE SHIP'S POSITION, AND THE G.P. FORM A TRIANGLE. IF YOU KNOW ANY TWO SIDES AND ONE ANGLE OF A TRIANGLE, OR ANY TWO ANGLES AND ONE SIDE, YOU CAN SOLVE ALL THE OTHER PARTS. YOU KNOW YOUR APPROXIMATE LATITUDE. SUBTRACTING YOUR LATITUDE FROM 90° WOULD GIVE YOU THE DISTANCE OF SIDE A OF THE TRIANGLE. YOUR LONGITUDE MINUS GHA WOULD GIVE THE INSIDE ANGLE AT THE POLE (ANGLE B) . NINETY DEGREES MINUS DEC. WOULD EQUAL THE DISTANCE OF SIDE C. WITH THOSE PIECES OF INFORMATION AND A SOLID UNDERSTANDING OF SPHERICAL TRIGONOMETRY; IT'S EASY TO LOCATE YOUR ACTUAL POSITION. DON'T GO AWAY. YOU WILL NOT HAVE TO WORK OUT THE TRIGONOMETRY PROBLEMS. MILLIONS OF THEM HAVE BEEN WORKED OUT FOR YOU AND PUBLISHED IN BOOKS KNOWN AS "SIGHT REDUCTION TABLES." ALL YOU'RE GOING TO DO IS PICK A READY-MADE PROBLEM WORKED OUT FOR A POSITION WITHIN THIRTY MILES OF YOUR DR, AND DO SOME PLAIN ARITHMETIC TO TAILOR THE PROBLEM TO FIT YOUR SITUATION.

   WHEN THE NAVIGATOR HAS TAKEN THE BASIC READINGS, THE SEXTANT ANGLE AND THE TIME HE TOOK IT, AND WRITTEN THEM DOWN ON HIS WORK- SHEET, HE IS READY TO START THE PROCEDURE KNOWN AS "SIGHT REDUCTION." THIS WILL INVOLVE LOOKING UP NUMBERS IN TWO BOOKS, THE "NAUTICAL ALMANAC" AND A SET OF TABLES YOU'LL GET TO KNOW AS "229." HE WILL DO SOME ARITHMETIC WITH THESE NUMBERS AND EVENTUALLY WIND UP WITH A LINE OR LINES OF POSITION ON THE CHART. WHY THIS STEP-BY-STEP PROCEDURE IS CALLED SIGHT "REDUCTION”, I DON'T KNOW. IT SEEMS MORE LIKE "EXPANSION" AS YOU WILL SOON SEE. BUT AS I SAID EARLIER, IT'S IMPORTANT TO STICK WITH THE "OFFICIAL" TERMS. THE SIGHT REDUCTION PROCESS CAN ONLY BE DONE STEP BY STEP. IN MOST CASES, THE STEPS MUST BE DONE IN A PARTICULAR ORDER. YOU CAN'T BEGIN STEP THREE WITHOUT THE ANSWERS YOU FOUND IN STEP TWO. THERE ARE ONE OR TWO SPOTS WHERE YOU COULD DO THE STEPS IN A DIFFERENT ORDER THAN  PRESENTED HERE, BUT WE HAVE CHOSEN THE SHORTEST AND MOST EFFICIENT ROUTE TO AVOID BACKTRACKING AND DUPLICATION OF WORK. THE EXCEPTION IS IN THE FIRST TWO STEPS; APPLYING THE CORRECTIONS TO THE SEXTANT READING AND CONVERTING THE WATCH READING TO CORRECT GREENWICH TIME. THESE ARE INDEPENDENT OF EACH OTHER,  SO WE WILL START WITH THE EASIER ONE, 

CORRECTIONS TO THE SEXTANT READING.